Diffusion maps for high-dimensional single-cell analysis of differentiation data
Open accessAbstract
Motivation: Single-cell technologies have recently gained popularity in cellular differentiation studies regarding their ability to resolve potential heterogeneities in cell populations. Analyzing such high-dimensional single-cell data has its own statistical and computational challenges. Popular multivariate approaches are based on data normalization, followed by dimension reduction and clustering to identify subgroups. However, in the case of cellular differentiation, we would not expect clear clusters to be present but instead expect the cells to follow continuous branching lineages. Results: Here, we propose the use of diffusion maps to deal with the problem of defining differentiation trajectories. We adapt this method to single-cell data by adequate choice of kernel width and inclusion of uncertainties or missing measurement values, which enables the establishment of a pseudotemporal ordering of single cells in a high-dimensional gene expression space. We expect this output to reflect cell differentiation trajectories, where the data originates from intrinsic diffusion-like dynamics. Starting from a pluripotent stage, cells move smoothly within the transcriptional landscape towards more differentiated states with some stochasticity along their path. We demonstrate the robustness of our method with respect to extrinsic noise (e.g. measurement noise) and sampling density heterogeneities on simulated toy data as well as two single-cell quantitative polymerase chain reaction datasets (i.e. mouse haematopoietic stem cells and mouse embryonic stem cells) and an RNA-Seq data of human pre-implantation embryos. We show that diffusion maps perform considerably better than Principal Component Analysis and are advantageous over other techniques for non-linear dimension reduction such as t-distributed Stochastic Neighbour Embedding for preserving the global structures and pseudotemporal ordering of cells. Availability and implementation: The Matlab implementation of diffusion maps for single-cell data is available at https://www.helmholtz-muenchen.de/icb/single-cell-diffusion-map. Contact: fbuettner.phys@gmail.com, fabian.theis@helmholtz-muenchen.de Supplementary information: Supplementary data are available at Bioinformatics online.
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Many of the methods described here are applicable across different single-cell data types.
“Many of the methods described here are applicable across different single-cell data types145.”
From Revealing the vectors of cellular identity with single-cell genomics (2016) · cites this paper as [145]
Diffusion map based on TOSICA attention embedding confirms two potential origins of cDC3_LAMP3 from cDC1s and cDC2-CXCL9.
“As interpretable trajectories, the diffusion map52 based on TOSICA attention embedding confirms two potential origins of the cDC3_LAMP3 from cDC1s and cDC2-CXCL9, as previously suggested48 (Fig. 4d).”
From Transformer for one stop interpretable cell type annotation (2023) · cites this paper as [52]
Moignard et al. used single-cell qPCR on mesodermal cells from 7- to 8-day-old mouse embryos; diffusion maps identified developmental pseudotime trajectories, recovering the ordering of known markers.
“Mesodermal cells from 7‐ to 8‐day‐old mouse embryos were analysed using single‐cell qPCR to understand the early development of blood lineages (Moignard et al, 2015). Here, diffusion maps were used to identify developmental pseudotime trajectories (Haghverdi et al, 2015), recovering correctly the ordering of known markers.”
From Using single-cell genomics to understand developmental processes and cell fate decisions (2018) · cites this paper as Haghverdi et al, 2015
PCA and diffusion maps are popular dimensionality reduction techniques that are principally summarization methods.
“Two popular dimensionality reduction techniques that are principally summarization methods are principal component analysis (PCA; Pearson, 1901) and diffusion maps (Coifman et al, 2005) which were popularized for single‐cell analysis by Haghverdi et al (2015).”
From Current best practices in single-cell RNA-seq analysis: a tutorial (2019) · cites this paper as Haghverdi et al (2015)
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- Authors
- Haghverdi, L., Buettner, F., & Theis, F. J.
- Affiliations
- Helmholtz Munich (DE)
- Corresponding author
- Buettner, Florian
- Theis, Fabian J.
- Venue
- Bioinformatics
- Publisher
- Oxford University Press (OUP)
- Published
- 2015-05-21
- Volume
- 31
- Issue
- 18
- Pages
- 2989-2998
- ISSN
- 1367-4803 (ISSN-L)
- 1367-4811
- OpenAlex
- W2128120736
- Cited by
- 649
- References
- 35
- Citations by year
- 2026: 36 · 2025: 49 · 2024: 59 · 2023: 61 · 2022: 59 · 2021: 72 · 2020: 71 · 2019: 87 · 2018: 70 · 2017: 44 · 2016: 36 · 2015: 4 · 2014: 1
- FWCI
- 22.28
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Bioinformatics (publishedVersion)
- PubMed (publishedVersion)
- MDC Repository (Max-Delbrueck-Center for Molecular Medicine) (submittedVersion)
- HighWire Press Open Archive (submittedVersion)
- Site cant be reached (submittedVersion)
- PuSH - Publication Server of Helmholtz Zentrum München (submittedVersion)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Single-cell and spatial transcriptomics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene expression and cancer classification
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Keywords
- diffusion maps, single-cell RNA sequencing, cell differentiation trajectories, kernel width selection, missing data, measurement noise, nonlinear dimensionality reduction, hematopoietic stem cells, embryonic stem cells, preimplantation embryo, pluripotency
- MeSH terms
- Algorithms, Animals, Blastocyst, Cell Differentiation, Diffusion, Gene Expression Regulation, Hematopoietic Stem Cells, Humans, Probability, Cluster Analysis, Principal Component Analysis, Mice, Embryonic Stem Cells, Single-Cell Analysis, High-Throughput Nucleotide Sequencing, Real-Time Polymerase Chain Reaction
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